“Agnostic atheism” is either nonsensical or superfluous: Presented in three cases.

It would seem some greater elucidation is required to explain more specifically why the phrase “agnostic atheist” in the weak case is nonsensical (and superfluous in the strong case). I am going assume a tabula rasa approach and start from the ground up in the most cogent step by step way I possibly can. If at any checkpoint you can not accept the argument and must STOP then feel free to message me and tell me why it is you can’t continue.

Defining of terms strictly for sake of this argument:

Weak atheism (weak case): Atheism defined as merely not having a belief in God. (“I do not believe God exist.”)
Strong atheism (Strong case): Atheism defined as believing or asserting that God does not exist. (“I believe God does not exist.”)
Agnostic: An epistemic modifier defined to be “I do not know”

Checkpoint #1: Review stipulative defining of terms for the purpose of this entry. If you accept them then continue on, If you do not accept them then STOP.

Assumptions:

God should be inferred to also include the plural form “Gods” (without any loss of generality)
Acceptance of belief condition in weak form: ~(Kap → Cap) ^ (Kap → Bap). (To be understood as knowledge does not entail certainty and knowledge entails belief
Belief does not entail knowledge: (Bap →/ Kap) (“I believe p is true” does not mean “I know p is true)
Juxtaposing two words, the first word is modifying the second word, and that the whole term is a subset (not a proper subset as will see in case #3) of the second term. i.e. Agnostic atheist means agnostic modifies atheist and “agnostic atheist” is a subset of “atheist”.

Checkpoint #2: Review assumptions. If you accept them then continue on to Case #1, If you do not accept them then STOP.

Case #1 -(Literal interpretation)

Assume: Weak atheism

Agnostic atheist would be an weak atheist with the epistemic modifier of agnostic modifying the word “atheist”.

“I do not know” + “I do not believe God exist”= “I do not know I do not believe God exist”

Which is nonsensical as you certainty would know if you do or do not believe God exist.

Checkpoint #3: Review Case #1. If you accept “agnostic atheist” is nonsensical (in the weak case) you can continue to Case #2 if you do not accept it as nonsensical then STOP.

Case #2

Assume: Weak atheism

p1) Atheism in the weak case is not a belief position as defined as “I do not believe God exists”.
p2) Knowledge is a subset of belief (from the belief condition in the weak form)
c) If atheism in the weak case is not a belief position then it follows that it can not be modified by knowledge (from p2) (it is nonsensical)

Example: Fords are a subset of cars. You can not modify a non-car with “Ford” as you first have to have a car before you can say what type of car it is, as “Ford” is a subset of “car”.

Checkpoint #4: Review Case #2. If you accept “agnostic atheist” is nonsensical (in the weak case) you can continue on to Case #3. If you do not accept Case #2 as nonsensical then STOP.

Case #3 – (As epistemic modifier/non-literal interpretation)

Assume: Strong Atheism

p1) Atheism in the strong case: “I believe God does not exist.”
p2) Agnostic: “I do not know”
p3) Atheism in the strong case makes no statement about knowledge (from the belief condition in the weak form)
p4) Agnostic atheism: “I believe God does not exist and I do not know” (As epistemic modifier/non-literal interpretation)
C1) Agnostic atheism infers “I believe does not exist, but not making a statement about knowledge” (from p3-p4)
P5) Atheism in the strong case infers: “I believe God does not exist, but not making a statement about knowledge” (from p1&p3)
C) Atheism in the strong case infers the same thing as “agnostic atheist”. (“Agnostic” in “agnostic atheist” is therefore superfluous)

Checkpoint #5: Review Case #3. If you accept “agnostic atheist” is superfluous (in the strong case) you can continue on. If you do not accept Case #3 and that “agnostic atheist” is superfluous (in the strong case) then STOP.

I have presented 3 arguments, two of which show conclusively that “agnostic atheist” in the weak case is nonsensical and one showing conclusively that “agnostic atheist” in the strong case is superfluous. If you have agreed with any or all of these cases please let me know, and if you have not agreed please give specifics as to what premise you reject and why.